# The center of a circle lies on the line y = 3x + 1 and is tangent to the x-axis at (−2,0) . What is the equation of the circle in standard form? You don't have to give me the answer, but at least please help me understand what it is that I need to be looking for in order to solve this problem (step-by-step if it's possible), I'm stuck.

(x + 2)² + (y + 5)² = 25

Step-by-step explanation:

The circle is tangent to the x-axis at (-2, 0).  This means the center of the circle must be directly above or below this point.  So the x-coordinate of the center is -2.

Since the center of the circle is on the line y = 3x + 1, we can find the y-coordinate:

y = 3(-2) + 1

y = -5

The center of the circle is (-2, -5).  The distance between the center and the point (-2, 0) is 5 units.  This is the radius of the circle.

We can now write the equation of the circle:

(x − h)² + (y − k)² = r²

(x + 2)² + (y + 5)² = 25

Graph:

desmos.com/calculator/wzionolfli

Th equation of the circle will be (x + 2)² + (y + 5)² = 25.

What is a circle?

A circle is a two-dimensional geometry on the plane having a centre point and the circular line is drawn equidistant from the centre point.

At, the circle is perpendicular to the x-axis (-2, 0). Therefore, the circle's centre must be located directly above or below this point. Therefore, the centre's x-coordinate is -2.

We can determine the y-coordinate because the circle's centre lies on the line y = 3x + 1:

y = 3(-2) + 1

y = -5

The circle's nucleus is (-2, -5). The centre is located 5 units away from the point (-2, 0). This is the circle's radius.

We can now write the equation of the circle:

(x − h)² + (y − k)² = r²

(x + 2)² + (y + 5)² = 25

Therefore, the equation of the circle will be (x + 2)² + (y + 5)² = 25.

To know more about the equation of a circle follow

brainly.com/question/1506955

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## Related Questions

How to find area of circle when circumference is given​

Answer: Since you have the circumference of the circle already you should plug the circumference into the formula of the radius: r=C/2π, once you find the radius plug it into the area of a circle formula:a=πr^2. By utilizing the circumference of the circle you were able to find the area of it

C- circumference

a-area

Which answer shows a correct order to solve this story problem? Maurine had to pay \$2.52 tax on her purchases. She bought 3 books for \$12.99 each, 2 pens for \$0.69 each, and a magazine for \$2.99. How much did Maureen spend?

A.
Step 1: Add the price of a book and a pen.
Step 2: Multiply by 3 and then by 2.
Step 3: Add \$2.99 to that result.
Step 4: Add the tax to the total of the purchases.

B.
Step 1: Calculate the total price of the 2 pens.
Step 2: Add \$2.99 to that total.
Step 3: Calculate the total price of the 3 books.
Step 4: Add the tax to the price of the 3 books

C.
Step 1: Calculate the total price of the 3 books.
Step 2: Calculate the total price of the 2 pens.
Step 3: Add \$2.99 to the total of the cost of the books and pens.
Step 4: Add the tax to the total of the purchases.

D.
Step 1: Add \$2.99 to the amount of the tax.
Step 2: Calculate the total price of the 2 pens.
Step 3: Calculate the total price of the 3 books.
Step 4: Add the prices of the pens to the price of the books.
Question

C is correct.
1. You do 12.99 times 3
2. \$0.69 times 2
3. Add \$2.99 to the two prices above
4. Add the \$2.52 tax to the prices
And you should get around \$45 and some change

The ratio of boys to girls in a class is 1:2. If there are 51 students in the class, how many boys are there?

17

Step-by-step explanation:

The ratio of boys to girls is 1:2

The total ratio of students in the class is 1+2 = 3

Since there are 51 students in the class therefore, the number of boys in the class is 1/3 × 51

= 17

Gcf of 63 and 27 i will give toy 12pts